与内切圆相关的特殊点

GeoGebra 命令及参数

1. Line(A, B) → a
2. Line(B, C) → b
3. Line(C, A) → c
4. Incircle(A, B, C) → d
5. Center(d) → Incenter
6. Intersect(d, a, 1) → D
7. Intersect(d, c, 1) → E
8. Intersect(d, b, 1) → F
9. Segment(A, F) → e
10. Segment(D, C) → f
11. Segment(B, E) → g
12. Intersect(e, f) → Gergonne
13. AngularBisector(c, a) → h, i
14. AngularBisector(c, b) → j, k
15. Intersect(h, k) → G
16. Intersect(h, j) → H
17. Intersect(i, j) → I
18. OrthogonalLine(G, c) → l
19. OrthogonalLine(H, a) → m
20. Intersect(c, l) → J
21. Circle(G, J) → p
22. Intersect(a, m) → K
23. Circle(H, K) → q
24. OrthogonalLine(I, c) → n
25. Intersect(c, n) → L
26. Circle(I, L) → r
27. Intersect(p, a, 1) → M
28. Intersect(q, c, 1) → N
29. Intersect(r, b, 1) → O
30. Segment(M, C) → s
31. Segment(A, O) → t
32. Segment(B, N) → a_1
33. Intersect(s, t) → Nagel
34. Midpoint(A, B) → P
35. Midpoint(B, C) → Q
36. Midpoint(C, A) → R
37. Incircle(P, Q, R) → c_1
38. Segment(P, R) → b_1
39. Segment(R, Q) → d_1
40. Segment(Q, P) → e_1
41. Center(c_1) → Spieker